A rigorous proof of the Landauer–Büttiker formula

Cornean, Horia D.; Jensen, Arne; Moldoveanu, V.

doi:10.1063/1.1862324

Cited by 65 publications

(49 citation statements)

References 32 publications

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“…In practical applications one usually adds a factor of two which accounts for the spin states of the electron, in other words the right-hand side of (2.9) is multiplied in the standard units by 2e 2 / h. A rigorous derivation of the Landauer-Büttiker formula together with a bibliography can be found in [CJM05]. Let us add that such a description of transport contains two simplifying assumptions.…”

Section: Notesmentioning

confidence: 99%

Quantum Waveguides

Exner

Kovařík

2015

Theoretical and Mathematical Physics

137

133

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More information about this series at http://www.springer.com/series/720The series founded in 1975 and formerly (until 2005) entitled Texts and Monographs in Physics (TMP) publishes high-level monographs in theoretical and mathematical physics. The change of title to Theoretical and Mathematical Physics (TMP) signals that the series is a suitable publication platform for both the mathematical and the theoretical physicist. The wider scope of the series is reflected by the composition of the editorial board, comprising both physicists and mathematicians. The books, written in a didactic style and containing a certain amount of elementary background material, bridge the gap between advanced textbooks and research monographs. They can thus serve as basis for advanced studies, not only for lectures and seminars at graduate level, but also for scientists entering a field of research.

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Section: Notesmentioning

confidence: 99%

Quantum Waveguides

Exner

Kovařík

2015

Theoretical and Mathematical Physics

137

133

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“…There are by now several proofs of the Landauer-Büttiker formula in the NESS approach (see [4,28]), and in the finite volume regularization approach (see [14][15][16]). Here we give yet another proof in the NESS approach.…”

Section: The Case Of Sudden Couplingmentioning

confidence: 99%

The Effect of Time-Dependent Coupling on Non-Equilibrium Steady States

Cornean

Neidhardt

Zagrebnov

2009

Ann. Henri Poincaré

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30 pagesInternational audienceConsider (for simplicity) two one-dimensional semi-infinite leads coupled to a quantum well via time dependent point interactions. In the remote past the system is decoupled, and each of its components is at thermal equilibrium. In the remote future the system is fully coupled. We define and compute the non equilibrium steady state (NESS) generated by this evolution. We show that when restricted to the subspace of absolute continuity of the fully coupled system, the state does not depend at all on the switching. Moreover, we show that the stationary charge current has the same invariant property, and derive the Landau-Lifschitz and Landauer-Buttiker formulas

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“…Unfortunately due to the fact that in this case the "perturbation" is not localized the problem is much more difficult and it has been worked out only at the linear response theory level. In this context the Landauer-Büttiker formula has been shown to hold true at the heuristic level by Baranger and Stone [7] and rigorously proved for a tight-binding model for reservoirs by Cornean, Jensen and Moldoveanu [10].…”

Section: Introductionmentioning

confidence: 99%

Independent electron model for open quantum systems: Landauer-Büttiker formula and strict positivity of the entropy production

Nenciu

2007

Journal of Mathematical Physics

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A general argument leading from the formula for currents through an open noninteracting mesoscopic system given by the theory of nonequilibrium steady states (NESS) to the Landauer-Büttiker formula is pointed out. Time reversal symmetry is not assumed. As a consequence it follows that, as far as the system has a nontrivial scattering theory and the reservoirs have different temperatures and/or chemical potentials, the entropy production is strictly positive.

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A rigorous proof of the Landauer–Büttiker formula

Abstract: Abstract. Excitons in carbon nanotubes may be modeled by two oppositely charged particles living on the surface of a cylinder. We derive three one dimensional effective Hamiltonians which become exact as the radius of the cylinder vanishes. Two of them are solvable.

Cited by 65 publications

References 32 publications

Quantum Waveguides

Quantum Waveguides

The Effect of Time-Dependent Coupling on Non-Equilibrium Steady States

Independent electron model for open quantum systems: Landauer-Büttiker formula and strict positivity of the entropy production

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